Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur

Kevin Egan; Yu-Ting Tseng; Nicolas Holzschuch; Frédo Durand; Ravi Ramamoorthi

inria-00388461, version 1

Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur

Kevin Egan ()^a^, 1, Yu-Ting Tseng^a^, 1, Nicolas Holzschuch ()^b^, 2, Frédo Durand^c^, 3, 4, Ravi Ramamoorthi^d^, 5

ACM Transactions on Graphics 28, 3 (2009) 93:1-14

Abstract: Motion blur is crucial for high-quality rendering but is also very expensive. Our first contribution is a frequency analysis of motion-blurred scenes, including moving objects, specular reflections, and shadows. We show that motion induces a shear in the frequency domain, and that the spectrum of moving scenes is usually contained in a wedge. This allows us to compute adaptive space-time sampling rates, to accelerate rendering. For uniform velocities and standard axis-aligned reconstruction, we show that the product of spatial and temporal bandlimits or sampling rates is constant, independent of velocity. Our second contribution is a novel sheared reconstruction filter that tightly packs the wedge of frequencies in the Fourier domain, and enables even lower sampling rates. We present a rendering algorithm that computes a sheared reconstruction filter per pixel, without any intermediate Fourier representation. This often permits synthesis of motion-blurred images with far fewer rendering samples than standard techniques require.

a – Columbia University
b – INRIA
c – MIT
d – UC Berkeley
1: Department of Computer Science [New York]
Columbia University
2: ARTIS (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
CNRS : UMR5224 – INRIA – Laboratoire Jean Kuntzmann – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
3: Massachusets Institute of Technology (MIT)
MIT
4: Computer Science and Artificial Intelligence Laboratory (CSAIL)
Massachussetts Institute of Technology (MIT)
5: Electrical Engineering and Computer Science [Berkeley] (EECS)
University of California, Berkeley

inria-00388461, version 1
http://hal.inria.fr/inria-00388461
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From: Nicolas Holzschuch <>
Submitted on: Tuesday, 26 May 2009 17:04:54
Updated on: Sunday, 17 March 2013 23:59:38

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DOI: 10.1145/1531326.1531399

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%% inria-00388461, version 1
%% http://hal.inria.fr/inria-00388461
@article{egan:inria-00388461,
    hal_id = {inria-00388461},
    url = {http://hal.inria.fr/inria-00388461},
    title = {{Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur}},
    author = {Egan, Kevin and Tseng, Yu-Ting and Holzschuch, Nicolas and Durand, Fr{\'e}do and Ramamoorthi, Ravi},
    abstract = {{Motion blur is crucial for high-quality rendering but is also very expensive. Our first contribution is a frequency analysis of motion-blurred scenes, including moving objects, specular reflections, and shadows. We show that motion induces a shear in the frequency domain, and that the spectrum of moving scenes is usually contained in a wedge. This allows us to compute adaptive space-time sampling rates, to accelerate rendering. For uniform velocities and standard axis-aligned reconstruction, we show that the product of spatial and temporal bandlimits or sampling rates is constant, independent of velocity. Our second contribution is a novel sheared reconstruction filter that tightly packs the wedge of frequencies in the Fourier domain, and enables even lower sampling rates. We present a rendering algorithm that computes a sheared reconstruction filter per pixel, without any intermediate Fourier representation. This often permits synthesis of motion-blurred images with far fewer rendering samples than standard techniques require.}},
    language = {English},
    affiliation = {Department of Computer Science [New York] , ARTIS - INRIA Grenoble Rh{\^o}ne-Alpes / LJK Laboratoire Jean Kuntzmann , Massachusets Institute of Technology - MIT , Computer Science and Artificial Intelligence Laboratory - CSAIL , Electrical Engineering and Computer Science [Berkeley] - EECS},
    publisher = {ACM},
    pages = {93:1-14},
    journal = {ACM Transactions on Graphics},
    volume = {28},
    number = {3 },
    audience = {international },
    doi = {10.1145/1531326.1531399 },
    year = {2009},
    month = Aug,
    pdf = {http://hal.inria.fr/inria-00388461/PDF/mbshadow.pdf},
}

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